Sunday, August 24, 2014

Found normal distributions in price changes and price decrement frequencies

I've been measuring the distribution of negative fluctuations in forex market history for the EUR_USD. I discovered that most variations in price (from one instant to another, with a time base of 1 minute) are "small", when compared to larger ones. Sudden, large increments or decrements are scarce. The following plot shows the data from sorted (smallest to largest) price changes (both positive and negative) along many weeks (each week has a different color).

The plot shows a large amount of "small" values near the center (which is zero), and only a few large ones near the sides. This implies that a lapse in time with a high density of price decrements has more probability of containing large negative price fluctuations than a lapse with few price decrements.

To extract the frequency of decrements at any point in time, only the direction of the currency price is required. The following picture shows price decrements in red, and increments in green. Blank spaces represent unknown currency fluctuations in a given instant. What I try to find here is how many red squares there are within a given window. Then I shift that window to the right, and count the red squares again. I keep shifting and counting until I reach the end of the data set.

Interestingly, it turns out the set of frequencies (sampled by shifting the window from top-left to bottom-right) also have a normal distribution. This means there are more "small" frequencies than "big" ones in all consecutive windows of time.

Plotting the histogram for both data-sets showed an approximate normal (Gaussian) distribution.

This shows that the variations in price are mostly smooth, with occasional outbursts. That is: they are more likely to fluctuate within a given (relatively) small range at any given instant. There is a certain stability in currency price change.